title: Do baseline P-values follow a uniform distribution in randomised trials?
abstract: BACKGROUND
  The theory has been put forward that if a null hypothesis is true, P-values should follow a Uniform distribution. This can be used to check the validity of randomisation.
  
  
  METHODS
  The theory was tested by simulation for two sample t tests for data from a Normal distribution and a Lognormal distribution, for two sample t tests which are not independent, and for chi-squared and Fisher's exact test using small and using large samples.
  
  
  RESULTS
  For the two sample t test with Normal data the distribution of P-values was very close to the Uniform. When using Lognormal data this was no longer true, and the distribution had a pronounced mode. For correlated tests, even using data from a Normal distribution, the distribution of P-values varied from simulation run to simulation run, but did not look close to Uniform in any realisation. For binary data in a small sample, only a few probabilities were possible and distribution was very uneven. With a sample of two groups of 1,000 observations, there was great unevenness in the histogram and a poor fit to the Uniform.
  
  
  CONCLUSIONS
  The notion that P-values for comparisons of groups using baseline data in randomised clinical trials should follow a Uniform distribution if the randomisation is valid has been found to be true only in the context of independent variables which follow a Normal distribution, not for Lognormal data, correlated variables, or binary data using either chi-squared or Fisher's exact tests. This should not be used as a check for valid randomisation.
authors.affiliation: Department of Health Sciences, University of York, York, North Yorkshire, United Kingdom.
authors.forename: Martin
authors.initials: M
authors.lastname: Bland
mesh_terms: D006801:Humans; D016032:Randomized Controlled Trials as Topic / Q000379:methods*; D015203:Reproducibility of Results; D013223:Statistics as Topic / Q000379:methods*